$K$ is the midpoint of $\overline{JL}$ $J$ $K$ $L$ If: $ JK = 2x - 7$ and $ KL = 7x - 37$ Find $JL$.
Solution: A midpoint divides a segment into two segments with equal lengths. ${JK} = {KL}$ Substitute in the expressions that were given for each length: $ {2x - 7} = {7x - 37}$ Solve for $x$ $ -5x = -30$ $ x = 6$ Substitute $6$ for $x$ in the expressions that were given for $JK$ and $KL$ $ JK = 2({6}) - 7$ $ KL = 7({6}) - 37$ $ JK = 12 - 7$ $ KL = 42 - 37$ $ JK = 5$ $ KL = 5$ To find the length $JL$ , add the lengths ${JK}$ and ${KL}$ $ JL = {JK} + {KL}$ $ JL = {5} + {5}$ $ JL = 10$